Math  /  Trigonometry

QuestionSketch the least positive angle θ\theta for the line 7x+8y=0-7 x + 8 y = 0 (with x0x \geq 0) and find its six trig functions.

Studdy Solution
The cotangent of θ\theta is the reciprocal of the tangent of θ\theta.
cot(θ)=87\cot(\theta) = \frac{8}{7}So, the least positive angle θ\theta is arctan(78)\arctan\left(\frac{7}{8}\right), and the six trigonometric functions of θ\theta are sin(θ)=7113\sin(\theta) = \frac{7}{\sqrt{113}}, cos(θ)=8113\cos(\theta) = \frac{8}{\sqrt{113}}, tan(θ)=78\tan(\theta) = \frac{7}{8}, csc(θ)=1137\csc(\theta) = \frac{\sqrt{113}}{7}, sec(θ)=1138\sec(\theta) = \frac{\sqrt{113}}{8}, and cot(θ)=87\cot(\theta) = \frac{8}{7}.

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